Charge sharing correction methods for pixelated radiation detector arrays

ABSTRACT

Various aspects include methods of compensating for issues caused by charge sharing between pixels in pixel radiation detectors. Various aspects may include measuring radiation energy spectra with circuitry capable of registering detection events occurring simultaneous or coincident in two or more pixels, adjusting energy measurements of simultaneous-multi-pixel detection events by a charge sharing correction factor, and determining a corrected energy spectrum by adding the adjusted energy measurements of simultaneous-multi-pixel detection events to energy spectra of detection events occurring in single pixels. Adjusting energy measurements of simultaneous-multi-pixel detection events may include multiplying measured energies of simultaneous-multi-pixel detection events by a factor of one plus the charge sharing correction factor.

FIELD

The present application relates generally to radiation detectors for computed tomography imaging systems, and more specifically to methods for processing the output of pixelated radiation detectors.

BACKGROUND

In Single Photon Emission Computed Tomography (SPECT) imaging systems, gamma rays emitted from a source, such as a radiopharmaceutical or radiotracer, are detected by a detector array, such as a cadmium zinc telluride (“CZT”) detector. Other direct conversion detectors employing cadmium telluride (CdTe), gallium arsenide (GaAs), or silicon (Si), or any indirect director based on a scintillator material, may also be used in SPECT imaging systems. Images taken at different angles are joined together to reconstruct 3-dimensional images of the object under examination.

The electrical signal generated by solid state radiation detectors, such as CZT detectors, results from gamma-rays exciting electrons in the atoms of the material that ejects electrons from their orbits and into a conduction band of the bulk material. Each electron ejected into the conduction band leaves behind a net positive charge that behaves like a positively charged particle known as a “hole” that migrates through the material in response to an electric field applied between a cathode and an anode. Electrons in the conduction band are attracted by the resulting internal electric field and migrate to the anode where they are collected creating a small current that is detected by circuitry, while the holes migrate towards the cathode.

Each gamma-ray will generate many electron-hole pairs, depending upon the energy of the photon. For example, the ionization energy of CZT is 4.64 eV, so absorbing the energy of a 140 keV gamma ray from Technetium will generate about 30,000 electron-hole pairs.

SUMMARY

Various aspects of the present disclosure provide methods of compensating for issues caused by charge sharing in pixel radiation detectors by addressing charge-sharing phenomena. Various aspects include measuring radiation energy spectra by a pixel radiation detector capable of registering simultaneous or coincident detection events occurring in two or more pixels, adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor, and determining a corrected energy spectra by adding the adjusted energy measurements of detection events occurring simultaneously in two or more pixels to energy spectra of detection events occurring in single pixels. In some aspects, determining the charge sharing correction factor may include creating a first energy spectra for detection events occurring in single pixels and determining its peak value Vpeak1, creating a second energy spectra for detection events occurring simultaneously in two or more pixels and determining its peak value Vpeak2, and calculating the charge sharing correction factor as (Vpeak1−Vpeak2)/Vpeak2. In some aspects, adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor may include multiplying measured energies of detection events occurring simultaneously into more pixels by a factor of one plus the charge sharing correction factor.

Various embodiments may be used to calibrate solid state radiation detectors, such as CZT detectors, during design development, during manufacturing, and/or periodically in service.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are presented to aid in the description of embodiments of the disclosure and are provided solely for illustration of the embodiments and not limitation thereof.

FIG. 1 is a block diagram of a Single Photon Emission Computed Tomography (SPECT) imaging system suitable for use with various embodiments of the present disclosure.

FIG. 2 is a conceptual cross section view diagram of a semiconductor pixel radiation detector illustrating gamma-ray interactions.

FIG. 3 is a conceptual top view diagram of a semiconductor pixel radiation detector illustrating gamma-ray interactions.

FIG. 4 a graph of cross-sections for photoelectric, Rayleigh scattering and Compton scattering interactions in a CZT detector as a function of photon energy.

FIG. 5 is a diagram of gamma ray interactions in a CZT detector may occur according to the photoelectric effect.

FIG. 6 diagram of Compton scattering.

FIG. 7 is a graph counts vs. energy illustrating contributions of primary gamma rays and scattered gamma rays in a total count of gamma rays measured by a radiation detector.

FIG. 8 diagram illustrating the relative path link of photo electrons versus emitted x-ray photons following photoelectric absorption of a gamma photon in a CZT detector.

FIG. 9 is a diagram illustrating expansion of an electron cloud due to diffusion and repulsion affects.

FIG. 10 is a conceptual cross section view diagram of a semiconductor pixel radiation detector illustrating gamma-ray interactions that lead to charge sharing between pixels.

FIG. 11 is a conceptual top view diagram of a semiconductor pixel radiation detector illustrating gamma-ray interactions that lead to charge sharing between pixels.

FIGS. 12A-12C are conceptual cross section view diagrams of a semiconductor pixel radiation detector illustrating migration of an electron cloud within an inter-pixel gap.

FIG. 12D is a notional graph illustrating charge sharing between adjacent pixels and the effects of charge loss for photon absorption events occurring in the inter-pixel gap.

FIG. 13A is a top view diagram of a semiconductor pixel radiation detector.

FIGS. 13B-13C are plots of energy spectra of detect events occurring simultaneously between center the pixel 6 and adjacent pixels 2, 5, 7, 10 shown in FIG. 13A.

FIGS. 14A and 14B are process flow diagrams illustrating methods of compensating for charge share affects in pixel radiation detectors according to various embodiments.

FIG. 15 is a component block diagram illustrating an example server suitable for use with the various embodiments.

DETAILED DESCRIPTION

The various embodiments will be described in detail with reference to the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. References made to particular examples and implementations are for illustrative purposes, and are not intended to limit the scope of the claims. Any reference to claim elements in the singular, for example, using the articles “a,” “an,” or “the” is not to be construed as limiting the element to the singular. The terms “example,” “exemplary,” or any term of the like are used herein to mean serving as an example, instance, or illustration. Any implementation described herein as an “example” is not necessarily to be construed as preferred or advantageous over another implementation. The drawings are not drawn to scale. Multiple instances of an element may be duplicated where a single instance of the element is illustrated, unless absence of duplication of elements is expressly described or clearly indicated otherwise.

Various embodiments of the present disclosure include methods for processing outputs of pixilated CZT radiation detectors used in gamma imaging systems to improve accuracy by accounting for errors due to charge sharing between pixels.

FIG. 1 is a functional block diagram of a SPECT imaging system 100. In a SPECT imaging system 100, a subject 102 (e.g., a patient) may be injected with a radiopharmaceutical containing a radioisotope, such as technetium 99, that is chemically configured to be absorbed by an organ or tumor to be examined creating a concentrated radiation source 104. The radiopharmaceutical within the source organ 104 emits gamma rays 106 that are detected by a digital radiation detector 108 within a gamma camera 110. Count and energy data from individual pixels within the digital radiation detector 108 are provided to an analyzer unit 112 that analyzes the detector data to determine the count and energy spectrum of detected gamma rays and provides the analyzed data to a digital imaging system computer 114. The analyzer unit 112 may apply calibration corrections including, for example, corrections for charges shared between pixels is determined according to various embodiments.

The SPECT imaging system 100 may also include additional structures, such as a collimator 120 within the gamma camera 110 and a robotic mechanism (not shown) that is configured to position the gamma camera 110 over the subject 102 at a variety of orientations (as illustrated in 130 and 140). Positioning the gamma camera 110 at various orientations with respect to the subject 102 enables gamma ray count and energy data to be acquired by the multi-pixel detector 108 from several different angles. Data collected in this manner can then be processed by the digital image system computer 114 to construct a 3D image of the organ or tumor 104 where the radiopharmaceutical has accumulated.

Various alternatives to the design of the SPECT imaging system 100 of FIG. 1 may be employed to practice embodiments of the present disclosure. For example, in industrial applications, such as luggage screening, the gamma source 104 may be positioned on a far side of the object being scanned with respect to the gamma camera and the gamma photons imaged by the detector 106 may be photons that have passed through the object instead of being emitted from the object. In such applications, the gamma source 104 and gamma camera 110 may be both rotated about the object, such as on a rotating frame or gantry. Further, various other types of systems that include a gamma camera that uses a solid-state pixilated radiation detector may benefit from various embodiments, particularly for calibrating the radiation detector during manufacture or in service.

The detector 106 of a SPECT imaging system may include an array of radiation detector elements, referred to as pixel sensors. The signals from the pixel sensors may be processed by a pixel detector circuit, such as an analyzer unit 112, which may sort detected photons into energy bins based on the energy of each photon or the voltage generated by the received photon. When a gamma photon is detected, its energy is determined and the photon count for its associated energy bin is incremented. For example, if the detected energy of a photon is 64 kilo-electron-volts (keV), the photon count for the energy bin of 60-80 keV may be incremented. The number of energy bins may range from one to several, such as two to six. The greater the total number of energy bins, the better the energy spectrum discrimination. Thus, the detector 106 of a gamma camera 110 provides information regarding both the location (within pixels) of gamma photon detections and the energy of the detected gamma photons.

FIG. 2 illustrates a cross-sectional view of two pixels 202 a, 202 b within a CZT radiation detector array 200. Such a detector 200 may include a sheet of CZT semiconductor crystal 208 on which are applied to a cathode 204 and the anodes 206 a, 206 b that define each pixel 202 a, 202 b. The anodes 206 a, 206 b may be spaced apart by an inter-pixel gap 210. In typical radiation detector arrays 200, the thickness of the CZT semiconductor crystal 208 may range from 1 mm to 20 mm, the anodes 206 a, 206 b may have a side dimension of 0.1 mm to 3 mm, and the inter-pixel gap 210 may range from 0.01 mm to 0.5 mm.

When a gamma-ray 220 is absorbed 222 by an atom within the CZT semiconductor crystal 208, a cloud of electrons 224 a are ejected into the conduction band of the semiconductor. Each ejected electron 224 creates a corresponding hole 225 of positive charge. A voltage is applied between the cathode 204 and anodes 206 a, 206 b causes the electrons 224 to drift to the anode 206 a where they are collected as a signal as described above. As described more fully below, diffusion and charge repulsion forces cause the electron cloud to expand (as shown at 226) by the time the electrons reached the anode 206 a. Holes 225 similarly migrate towards the cathode 204.

FIG. 3 is a top view of a portion of a pixelated radiation detector array 200 showing the plurality of pixels 202 a-202 aa formed by the anodes 206 a, 206 b positioned on the CZT semiconductor crystal 208. As described above, when a gamma-ray 220 interacts with atoms within the CZT semiconductor crystal 208, the ejected electrons 224 are gathered on the nearby anode 206 c, 206 f and recorded as a count. Further, the number of electrons 224 (i.e., charge) collected on the anode 206 c, 206 f is reflective of the energy of the incoming photon, and thus a measurement of the energy (or spectrum) of the detected photon can be determined from the charge or current detected on the anodes.

A fundamental problem with accurate energy resolution when using pixilated CZT radiation detectors is charge sharing between pixels. Charge sharing strongly depends on CZT inter-pixel gap properties, in particular on pixel to pixel spacing 210 and the nature of the surface passivation. Unless the surface passivation is ideal (which it never is), or the inter-pixel gap 210 very small (which cannot be accomplished using current manufacturing methods) there will be some charge-lost in the inter-pixel gap. Further, the amount of charge loss for photons interacting within the inter-pixel gap 210 depends upon the passivation process, which can vary from fabrication lot to fabrication lot, from detector to detector within a fabrication lot, and even from pixel gap to pixel gap. Consequently, a correction factor to account for inter-pixel gap charge loss may need to be determined (e.g., by a calibration test) for each detector at the time of manufacture (e.g., prior to shipment to the OEM customer). Such correction factors may also be determined for each inter-pixel gap to account for variations in surface passivation across each detector. Further, the inter-pixel gap charge loss may be temperature dependent, so such calibration testing may be performed over a range of operating temperatures for the detector. When performed during or after fabrication, the correction factor(s) determined during calibration testing may be stored in FLASH memory of the detector module so that the factor(s) can be retrieved and applied by the OEM manufacturer of the gamma camera and/or SPECT imaging system.

In a typical pixilated CZT detector, charge sharing can result in 10-15% count loss for pixels with a 500 um pixel pitch. Adding an inter-pixel steering grid (not shown) to reduce charge-sharing events would increase the input current leakage, and so does not work well in practice. Correcting for charge-sharing in signal processing typically requires either rejecting charge-sharing events or adding charge-sharing events by monitoring signals from the adjacent pixels. Rejection of the charge-shared events leads to loss of the detector efficiency, and so is typically not acceptable as reduced efficiency requires longer scan times and/or higher radiation doses. Adding neighboring charges does not work either due to charge-loss in the interpixel gap.

Charge sharing is typically an undesired phenomenon in imaging applications as the original charge induced in the CZT material is split between two or more pixels. As a result, the measured energy of the incoming photon is possibly registered with a wrong energy information and a wrong pixel location. However, when properly understood and analyzed, charge-sharing can actually lead to an improved spatial resolution and detector efficiency as provided for in various embodiments.

Gamma-ray photons can interact with the CZT material in various ways. The photons may be completely removed from the incident photon beam by absorption, may be scattered after the interaction, or may pass through the CZT detector without any deterioration of their energy. At low energies of interests, such as below 200 keV, and typical sensor thickness of 5 mm, most of the incoming radiation photons are either absorbed or scattered, the relative portion of each effect being highly dependent on the incoming photon energy.

The following three absorption and scattering effects are the most relevant: the photo-electric effect; Rayleigh scattering; and Compton scattering. The effective photon cross section in CZT of each effect is plotted in the graph 400 that is FIG. 4. Photo-electric effect (402) is dominant in the considered energy range of 20 to 200 keV, which is typical for medical imaging. Rayleigh scattering 404 is a dominant form of scattering at lower energies. At higher energies Compton scattering 406 becomes more probable. For example, a gamma-ray photon with an energy of 122 keV will interact with a CZT radiation detector via the photo-electric effect with an 82% probability, via the Rayleigh scattering with a 7% probability, and via the Compton scattering with a 11% probability. Due to the energy dependency of the cross sections for these three types of interactions, charge-sharing correction methods of various embodiments work the best at energies below 200 keV, working less well at higher energies due to Compton scattering.

The diagram 500 in FIG. 5 illustrates the photo-electric effect in which the energy of the interacting photon 502 is absorbed 504 by an electron that is ejected (referred to as a “photo-electron”) from its atom and the photon effectively disappears after the interaction. A complete absorption of the photon energy is the desired effect for CZT imaging. The name “photo-electron” comes from a process of ejecting an electron from one of the atomic shells of CZT. After the ejection of the photo-electron the atom is ionized. The vacancy in the bound shell is refilled with an electron from the surrounding medium or from an upper atom shell. This may lead either to the emission of one or more characteristic fluorescence X-rays 506 or to the ejection of an electron from one of the outer shells called an Auger electron.

Depending whether tellurium, cadmium or zinc atoms are involved the resulting fluorescence X-ray 506 energies might be in an 8 to 31 keV range (Te 27-31 keV; Cd 23-26 keV; Zn 8-10 keV). Therefore, in practical terms soft X-rays events may be detected if the detection threshold is at least 31 keV, which is typically the case. This is in particularly true in single-photon emission spectroscopy (SPECT) that uses standard isotopes like Technetium (^(99m)Tc) that emits a 140 keV photon. In addition, the projected distance 510 that the fluorescence X-rays 506 may travel in CZT is about 0.1 mm, which is much smaller than the typical pixel size of 2 mm. Therefore, while fluorescence generated soft X-rays 506 might show up in the tail of the measured CZT spectrum, such signals will likely not contribute significantly to charge sharing between pixels. However, it is worth noting that the generation of soft-X rays 506 affects the measured spectrum indirectly because the system will measure the energy of the absorbed photon as being less than the actual γ-photon energy by the amount of energy in the soft X-rays, thereby distorting the measured spectrum of radiation.

Rayleigh scattering involves photon scattering by atoms as a whole, frequently also called coherent scattering as the electrons of the atom contribute to the interaction in a coherent manner so that there is no energy transferred to the CZT material. The elastic scattering process changes only the direction of the incoming photon. Rayleigh scattering is a rather negligible effect in CZT SPECT imaging as it will not affect the measured energy spectrum, although it may lower the camera efficiency a bit.

Unlike Rayleigh scattering, Compton scattering involves photons that are scattered by free electrons and as a result lose some of their primary energy. The scattering diagram 600 in FIG. 6 illustrates that Compton scattering 600 occurs when an incoming photon 602 imparts some of its energy to a free electron 604 as kinetic energy, sending the electron along a path 608, with the resulting lower energy photon 606 scattering through an angle θ. This mechanism can contribute significantly to the measured CZT spectrum. The decrease in the photon energy that occurs in a Compton scattering event increases with increasing scattering angle θ. The energy and momentum lost by the photon 606 is transferred to one electron 604, called the recoil electron, which is emitted under a certain angle with respect to the direction of the incoming photon and can have a maximum kinetic energy defining as the so-called Compton edge. The Compton edge it is frequently visible in the spectrum measured by a CZT radiation detector as an abrupt end to the energy tail caused by Compton scattering.

The Compton scattering equation describes the change in photon energy and its corresponding wavelength as:

${\lambda^{\prime} - \lambda} = {\frac{h}{m_{e}c}\left( {1 - {\cos\;\theta}} \right)}$

where λ is the wavelength of the photon before scattering, λ′ is the wavelength of the photon after scattering, m_(e) is the mass of the electron, θ is the angle by which the photon's trajectory changes, h is Planck's constant, and c is speed of light. Substituting textbook values for m_(e), c and h, the characteristic Compton wavelength, defined as h/(m_(e)c), is found to be equal to 2.4 picometers (pm).

The Compton equation has two interesting properties. First, the characteristic Compton wavelength value is small compared to typical gamma ray wavelengths used in medical imaging (the wavelength of a 100 keV gamma ray is about 12 pm). As the result, the maximum wavelength change due to Compton scattering is only a fraction of the original wavelength. Secondly, the largest change in the photon energy can only be expected for scattering angles θ close to 180 degrees. Thus, the maximum wavelength change is twice the Compton wavelength change.

Compton scattering also occurs within the imaging subject in SPECT as well as in surrounding structures and the camera itself, raising the problem of distinguishing gamma photons that are coming from the subject of the imaging from gamma photons scattered off of other structures. Small angle Compton scattering diverts gamma photons through a small angle that may be acceptable for imaging, but reduces the gamma photon energy by only a small amount. In contrast, large angle Compton scattering, which would interfere with imaging, reduces the gamma photon energy by a significant amount. FIG. 7 illustrates in the graph 700 how the total number of gamma photons counted by the radiation detector (line 706) will be the combination of photons traveling directly from the radiation source to the detector (line 702 referred to as “primary” counts) and photons that have been scattered (line 704) and thus reached the detector from directions away from the radiation source. FIG. 7 also illustrates that the difference in spectrum of scattered photons compared to primary photons can be used to distinguish primary photons for imaging purposes by counting only those photons that have energies within an energy window 708 about the peak energy of the source gamma rays. FIG. 7 ignores the effect of charge sharing between pixels, which as described below, may result in a primary photon being measured by two or more pixels each at an energy that is less than the energy window due to energy being shared between the pixels.

Another factor affecting charge sharing between pixels is the size of the electron cloud generated when a photon is absorbed in the CZT detector. The term “cloud” is used to highlight the fact that the physical size of the electron charge is not a point but approximately a sphere with a certain radius. Each γ-ray photon absorbed in the CZT detector generates several thousands of electrons, so even the initial charge has finite physical dimensions. The number of generated electrons can be estimated by dividing the incoming photon energy by the CZT ionization energy of 4.64 eV. For example, a Technetium 99 gamma ray photon with an energy of 140 keV will produce about 30,000 electrons in the conduction zone, collectively carrying a charge of approximately 4.8 femto coulombs (fC).

Compton scattering of an incoming photon 802 may result in scattered photons interacting with CZT at several pixel sites. At each site of interaction, a Compton recoil electron or photoelectron will lose energy by generating a cloud of electrons by exciting electrons into the conduction band, creating electron-hole pairs.

Similarly, the photo-electric effect may result in interactions at several sites as illustrated in the diagram 800 in FIG. 8. When an incoming photon 802 is absorbed by an atom in the photo-electric effect, the ejected photoelectron carries with it the energy of the photon minus the binding energy of the particular electron ejected from the atom. The energy of the photoelectron is then dissipated as it excites electrons into the conduction band (and thus generates holes), creating a cloud of electrons 804 along its path of travel. The range of a photoelectron in CZT depends on the energy carried off by that electron. For example, a 40 keV photoelectron is stopped in CZT within about 10 μm, whereas a 100 keV photoelectron is stopped in CZT within about 47 μm. The clouds of electrons (and holes) generated by a photoelectron are not uniform in charge density, because electron-hole production increases towards the end of the track of the photoelectron. For a 100 keV photoelectron, 30% of the electron-hole pairs are created in the last 7 μm of its track through the CZT material. Additionally, an X-ray 806 of 25 keV may be produced in the initial interaction, and such an X-ray may have mean free path 810 of about 85 μm before it too is absorbed via the photo-electric effect. The electron cloud 808 generated by absorption of the X-ray 806 will add to the overall distribution of charge in the detector.

The proportions of interactions of gamma photons with the CZT detector via the photo-electric effect versus Compton scattering can be calculated using values from FIG. 4.

As the above discussion indicates, the process of electron cloud generation is rather complex and accurate predictions of the electron cloud size are difficult without resorting to comprehensive numerical methods. Monte-Carlo simulations indicate that although the size of the cloud varies with the incoming photon energy, it is generally small, ranging from a few microns for low energies to several micrometers at the higher energy end. For purposes of developing methods of the various embodiments, and initial electron cloud radius of 10 μm is presumed for photons with medium energies of 122 to 140 keV. Accurate knowledge of size of the initial electron cloud is not critical since the electron cloud is much larger by the time the charge drifts to the anode.

The electron cloud consists of several thousand individual electrons that drift towards the anode side of the detector. Since the distribution of electrons in the cloud is not uniform the electrons are subject to a diffusion process governed by Fick's diffusion law. In addition, electrons experience electrostatic repulsion from one another. Diffusion and repulsion act together to expand the electron cloud until the electrons reach the anode.

As described with reference to FIG. 2, the generated electron-hole pairs separate under the influence of the internal electric field created by the voltage applied between the anode and cathode, with the generated electrons moving toward the anode. The generated holes drift towards the cathode, but as hole mobility in CZT is very low, the effect of charge sharing between pixels is dominated by the electron movements. Thus, methods for accounting for charge sharing can assume that the generated holes do not move. The time required for electrons to separate from holes is in the order of a nanosecond and therefore can be neglected as well.

Referring to the diagram 900 in FIG. 9, as a photon-generated electron cloud 220 moves toward the anode 206, the size of the cloud will grow due to carrier diffusion and charge repulsion mechanisms. As the size of the electron cloud 226 grows due to these two effects, the electron cloud may start to become comparable to the pixel size, and thus induce charges on adjacent pixels. Depending on the threshold voltage settings of the SPECT read-out electronics, the charges within the electron cloud may be detected by more than one channel or pixel using spectroscopic electronics, such as a spectroscopic Application Specific Circuit (ASIC), capable of detecting events happening simultaneously in two or more pixel detectors.

As a result of the diffusion and repulsion processes, electron cloud spreads uniformly in size as schematically illustrated in FIG. 9. In the example shown in FIG. 9, the initial cloud is 67 μm wide with a characteristic sigma of 10 μm. By the time the cloud 226 reaches the anode 206 it is 190 μm wide. This spreading effect is highly dependent on the electric filed intensity. These dimensions of the electron cloud are examples and the actual dimensions of each electron cloud will vary depending upon the energy of the incoming gamma photon, the manner in which the gamma photon interacts with the detector materials, the temperature and pressure of the detector, and other factors.

Precise estimation of the diffusion spread can be obtained by numerically solving Fick's equation in a 3-D space. However, analytical approximations provide useful insight. For an initial delta function charge distribution (zero effective cloud size), the diffusion equation can be solved analytically to produce an effective sigma distance σ as: σ²=4Dt _(drift)  (1) where D is the diffusion coefficient of electrons in CZT and tdrift is a drift time from the initial interaction until the electron charge reaches the anode. The diffusion coefficient can be obtained using Einstein's relationship: D=μ _(n) kT/q  (2) where μn is electron mobility in CZT.

The drift time can be obtained assuming uniform electric field distribution in the CZT detector, the assumption that is typically valid within 95% of the detector body, as: t _(drift) =d ²/(μ_(n) V)  (3) where d is the detector thickness and V applied high voltage. Substituting (3) into (1) the following final expression is obtained: σ²=4kTL ² /qV  (4)

The final result in equation 4 reveals that the electron cloud spreading process is independent of the electron mobility value. This can be understood from the fact that while higher mobility leads to faster drift and shorter drift time it also leads to a higher diffusion constant through Einstein's relationship. The final result in equation 4 also indicates that the only physical parameters affecting the charge spreading process are the detector thickness L and the applied bias V since kT/q is a physical constant that is only mildly varying, as the CZT temperature is typically kept constrained in a tight range during detector operation.

For typical spectroscopic CZT detectors with thickness L of 5 mm and high-voltage bias V of 1000 V, the characteristic distance σ can be calculated from equation 4 as 50 μm. Thus, the electron cloud is about 150 μm assuming 3-sigma measure and that the electron distribution within the cloud is Gaussian. An electron cloud of 150 μm radius is comparable to the pixel size of 1.5-2.5 mm, which is the size of pixels typically being used in SPECT.

It should be noted that equations 1 and 4 are first order approximations that take into account only a diffusion process. A more elaborate formula that takes into account both diffusion and drift is:

$\begin{matrix} {{\Delta\sigma}_{x,y,z}^{2} = {2\left( {D + {\frac{1}{15}\left( \frac{3\mu\;{Ne}}{4{\pi ɛ}_{0}ɛ_{R}} \right)\frac{1}{\sqrt{5}\sigma_{x,y,z}}}} \right)\Delta\; t}} & (5) \end{matrix}$ where the first term D represents a diffusion process while the second term represents drift. N is the number of electrons in the charge cloud, e is the electron charge and εR is CZT relative permittivity. Note that equation 5 simplifies to equation 1 if the drift process is neglected. An interesting observation provided by equation 5 is that the drift repulsion effect increases with the number of electrons N, and thus, charge-sharing effects increase with the photon energy.

FIG. 10 is a cross-section diagram of two pixels 202 a, 202 b within a CZT detector 200 illustrating the various interactions and sources of cross sharing of charge clouds discussed above. As described with reference to FIG. 2, nominally gamma rays 220 will interact by the photoelectric effect and/or Compton scattering at one or more events 222, resulting in an electron cloud 224 a that drift towards the anode 206 a and a corresponding cloud of holes 225 that drift toward the cathode 204. As noted above, the electron cloud will expand in diameter due to diffusion and repulsion is shown at 226 a, but if the interaction 222 occurs away from the boundaries of the pixel 202 a, the entire charge of the electron cloud will be collected on the anode 206 a.

If the incoming gamma-ray 220 interacts with the CZT detector material via Compton scattering 1012 close to a boundary of a pixel 202 a, a recoil electron may produce a local electron cloud 1014 in that pixel 202 a, while the recoil gamma-ray follows a path 1010 that terminates in an adjacent pixel 202 b via a photoelectric effect event 1016 that ejects a photoelectron that produces an electron cloud 1018. In this situation, the charge resulting from the electron cloud 1014 generated by the Compton scattering event 1012 will be collected by the first pixel's anode 206 a, while the charge resulting from the electron cloud 1018 generated by the photoelectric affect event 1016 will be collected by the second pixel's anode 206 b. When this happens, counsel be recorded in both pixels 202 a, 202 b but with lower energies then that of the incoming gamma ray 220.

If the incoming gamma-ray 220 interacts with the CZT detector material via the photo electric effect close to a boundary of a pixel 202 a as illustrated in event 1022, the resulting electron cloud 1024 may expand under diffusion and repulsion processes to encompass both the anode 206 a of that pixel (portion 1026 a) and the anode 206 b of the adjacent pixel 202 b (portion 1026 b). Additionally, some of the charge in the expanded electron cloud may be trapped in surface defects within the CZT material 208 between the two pixels (portion 1026 c). Such charge sharing will result in signals recorded on two pixel anodes 206 a, 206 b for the single absorption event 1022, but at energies lower than that of the incoming photon 220.

Some incoming gamma-rays 220 will also interact with the CZT detector material between two pixels 202 a, 202 b as illustrated in event 1030, because the pixels are positioned a finite distance apart. In some cases, the resulting electron cloud 1032 may expand under diffusion and repulsion processes sufficient to encompass both anodes 206 a, 206 b, with some of the charge in the expanded electron cloud being trapped in surface defects within the CZT material 208 between the two pixels. In such cases, the charge sharing will result in signals recorded on two (or more) pixel anodes 206 a, 206 b for the single absorption event 1022, but at energies lower than that of the incoming photon 220. In other cases, such as when the inter-pixel photon interaction 1030 occurs near the anodes 206 a, 206 b, there may be insufficient time for the resulting electron cloud 1032 to expand sufficiently to encompass one or both of the adjacent anodes 206 a, 206 b, in which case the charge may be trapped in surface defects of the inter-pixel material 208 with no count.

FIG. 11 illustrates the charge sharing events from a top view of a pixelated CZT radiation detector 200. In addition to the absorption of events with electron clouds 224 retained within the pixels described with reference to FIG. 2, some gamma rays will interact with the detector 200 between pixels or close to the boundary of axles resulting in charge sharing between two or more pixels. For example, a photon absorbed between two pixels as illustrated in event 1102 may result in the electron cloud 1102 being shared between the two adjacent pixels 202 a, 202 b. As another example, a gamma-ray photon 220 may generate a first electron cloud 1104 in a first pixel 202 d via a Compton scattering event and generate a second electron cloud 1106 when the recoil photon is absorbed a second pixel 202 i such as via the photoelectric effect. As a further example, a gamma-ray photon 220 may be absorbed within the inter-pixel volume between three or four pixels 202 i, 202 j, 202 m, 202 n, in which case some of the resulting electron cloud 1108 may be absorbed in any one or all of the adjacent pixels, as well as within surface defects within the inter-pixel space.

Charge sharing effects that may occur when photon interactions occur within the inter-pixel volume is further illustrated in FIGS. 12A-12C.

Referring to FIG. 12A, a charge cloud 1224 generated due to a gamma-ray interaction within an inter-pixel gap but close to the CZT cathode close to the boundary of a pixel 202 a, the charge 1226 may drift towards only one pixel 202 a under the influence of the applied electric field that pixel's anode 206 a.

Referring to FIG. 12B, a charge cloud 1224 generated due to a gamma-ray interaction close to the CZT cathode and towards the middle of an inter-pixel gap, the charge 1226 may split under the influence of the magnetic field generated by the anodes 206 a, 206 b of adjoining pixels 202 a, 202 b, resulting in two charges 1226 a, 1226 b that may be detected by the respective pixels. As the charge 126 is split into two charges 1226 a, 1226 b, the signals measured by the pixels 202 a, 202 b will be less than present in the initial charge cloud 1224 and may not be equal.

The movement of charges illustrated in FIGS. 12A and 12B somewhat simplistic because the illustrations neglect surface effects at the inter-pixel gap. Experimental data has confirmed that imperfections in the surface passivation of the CZT material in the inter-pixel gap surface can result in absorption of some of the charge cloud that falls within the gap. This is illustrated in FIG. 12C, which shows that a portion 1226 c of the charge drifting in the inter-pixel gap is trapped by a surface region. Modeling of the portion of the charge trapped by the surface region in the inter-pixel gap is difficult as the electric field there has both vertical and lateral components. In addition, the surface region may contain significant number of trapping sites (surface shallow and deep level traps) due to imperfect passivation of the CZT material. However, some simplifying assumptions may enable estimating the effects of this charge-loss phenomena. At the surface, electrons experience a small electric field in the lateral (anode to anode) direction compared to the vertical (cathode to anode) direction field that drove movement from the place of the photon interaction. However, the electron cloud is still subject to the diffusion process, and as long as the electron cloud remains at or near the surface of the inter-pixel gap the charge will diffuse towards the adjacent pixels even if the cloud is much closer to one of the pixels than the other. The exact portion of the charge going to the adjoining pixels may be estimated based on the physical position of the cloud with respect to the two pixels 202 a, 202 b.

FIG. 12D illustrates graphically how the amount of charge loss due to charges being trapped by the surface region in the inter-pixel gap may affect the amount of charge gathered and thus detected photon energy (keV) measured by adjacent pixels. The graph 1240 illustrates how when there is no charge loss due to surface effects or deep traps (line 1244), the sum of the energies measured in the adjoining pixels will equal the actual energy E0 of the detected photon (i.e., E0=E1+E2). When the inter-pixel gap exhibits some charge loss (lines 1246 and 1248), the sum of the energies measured in the adjoining pixels (i.e., E1+E2) will be less than the energy of the detected photon due to the charge loss (CL), and thus E0=E1+E2+CL. Further, the effect of inter-pixel charge loss is greatest when photons are stopped in the middle between two pixels (i.e., close to where E1=E2), and decreases toward zero as the measured energy is increasingly measured in just one pixel. For detectors that exhibit a small inter-pixel gap charge loss as illustrated in line 1246, the charge loss CL may be small enough that the photon energy E0 is approximately equal to the sum of the energies measured by two pixels (i.e., E0≈E1+E2). However, for detectors that exhibit a large inter-pixel gap charge loss as illustrated in line 1246, as may be the case for detectors with a relatively large inter-pixel space and/or poor surface passivation, the charge loss CL may be significant, leading to errors in measured spectrum.

Experiments using Cd_(0.9)Zn_(0.1)Te detectors with various thickness (from 2 mm to 5 mm) made using various ways of manufacturing the passivation and measured with either spectroscopic or photon counting electronics, measured inter-pixel charge loss to be 10-15%, although occasionally much larger losses were observed for large (relative to the pixel size) inter-pixels gaps. The inter-pixel charge losses were dominated by double-pixel events as triple and multiple events (more than 3 pixels triggered at the same time such as 1108 in FIG. 11) were observed to be insignificant with low numbers of detected events.

In experiments, charge sharing results were obtained using a ⁵⁷Co source illuminating two different 4×4 pixel array detectors having the configuration illustrated in FIG. 13A. One array detector had a gap between the pixel electrodes of 0.1 mm, and the other array detector had a gap of 0.46 mm, both with a 2.46 mm pixel pitch. In these experiments, the pixel count data were recorded with a bias voltage of −300V and −800V at a temperature of 22° C. The average total electronic noise for the setup was 2.5 keV FWHM. The energy resolution of the detector samples (for the single pixel events) for all pixels was measured to vary between 5 and 9 keV FWHM at the 122 keV peak. Charge sharing events between pixels were observed by detecting coincident events in adjacent pixels. The time coincident spectra were recorded with a bias voltage of −800V at a temperature of 22° C. Plots of shared events between center pixel 6 and adjacent pixels 2, 5, 7 and 10 in FIG. 13A that were observed in experiments are presented in FIG. 13B for the array detector with a gap between the pixel electrodes of 0.46 mm, and in FIG. 13C for the array detector with a gap between the pixel electrodes of 0.1 mm.

Comparing FIGS. 13B and 13C, a clear pulse height loss for charge shared events appears most pronounced for the detector with the larger pixel gap (FIG. 13B). This effect is illustrated in FIGS. 13B and 13C using a 2D representation that gives the pulse height of shared events between one pixel (i.e., pixel 6 in FIG. 13A) and its neighbors (i.e., pixels 2, 5, 7 and 10 in FIG. 13A).

Ideally, the sum of the energies recorded as shared events by two pixels should add up to the full energy E0=E1+E2, as illustrated in line 1244 of FIG. 12D. This would be showing in FIGS. 13B and 13C as a straight line E2=E0−E1. That is approximately the case in FIG. 13C for the inter-pixel gap of 100 um, although some slight departure from linearity can be observed, as illustrated in line 1246 in FIG. 12D. However, the 2D plots in FIG. 13B show a clear bending for the 0.46 mm gap data. The curvature shows that the shared events do not have 100% efficient charge collection and that charge loss is the largest for those events that are stopped in the middle between two pixels, as illustrated in line 1248 in FIG. 12D. Moreover, this charge loss increases with the pixel gap. The results indicate that charge from the events stopped in between the pixels (e.g., events 1030 in FIG. 10) in detector arrays with large gaps between pixels will end up in the surface layer between the pixels and that charge effectively is trapped there. These events will therefore not induce their full signal in the pixel electrodes leading to errors in measured spectrum.

The result of this analysis and experimental data were used to develop the embodiment methods for accounting charge sharing between pixels of a pixelated radiation detector.

FIG. 14A illustrates a method 1400 for calibrating pixel radiation detectors and adjusting the output of such detectors to account for charge sharing effects according to various embodiments. The method 1400 may be implemented by a processor of a computing device (e.g., the computer 112 of FIG. 1 or the computing device 1500 of FIG. 15).

In step 1402, the processor may measure the energy spectra of radiation received on a pixel radiation detector from an Am241 or Co57 source using any suitable spectroscopic ASIC device that has capability to register simultaneous, coincidence events on multiple pixels.

In step 1404, the processor may create a first energy spectra for detection events occurring in single pixels and determining its peak value V_(peak1). In some embodiments, the processor may create the first spectra for the non-charge-shared events detected by the spectroscopic ASIC device, and use the results to determine a peak value V_(peak1) using normal analysis algorithms.

In step 1406, the processor may create a second energy spectra for detection events occurring simultaneously in two or more pixels and determining its peak value V_(peak2). In some embodiments the processor may create the second spectra for all charge-shared events detected by the spectroscopic ASIC device, and use the results to determine a peak value V_(peak2).

In step 1408, the processor may determine a charge sharing correction factor (CSCF) as a function of the photon energy in adjoining pixels using data obtained from calibration data, such as illustrated in FIGS. 13B and 13C. As illustrated in FIG. 12D, inter-pixel charge loss will be greatest when the charges measured by the adjoining pixels is equal or nearly equal, and decreases asymptotically as the difference in measured energy between the two pixels increases. Thus, the photon energies measured in adjacent pixels in a two-pixel charge-sharing scenario will be divided between the two pixels minus the charge loss. For example, if the photon energy is 60 keV, the measured energies between the two pixels may be 24 keV and 34 keV or 25 keV and 35 keV. When the energies measured in the adjacent pixels is equal, the charge loss (say 10 keV) will be greatest, so the 60 keV photon will be measured as two photons of 25 keV in adjoining pixels with 10 keV consumed by the inter-pixel charge loss. When the energies are not equally divided between the two pixels, the inter-pixel gap charge loss will be smaller. For example, the 60 keV photon might be measured as two photons of 20 keV and 32 keV in the adjoining pixels with 8 keV consumed by the inter-pixel charge loss. The closer the measured energy in one pixel approaches that of the absorbed photon, the less the energy that will be consumed by the inter-pixel charge loss. By collecting data on measured energies in adjoining pixels from inter-pixel gap events during a calibration exposure, a charge sharing correction factor can be determined that accounts for observed charge sharing losses.

In step 1410, the processor may adjust energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor. In particular the processor may multiply the energy of all detected charge-shared events by (1+CSCF), effectively shifting the energy of these events to the higher energies by the correction factor. For example, the charge sharing correction factor may shift energies of inter-pixel events by 10-15%.

In step 1412, the processor may determine a corrected energy spectrum by adding the adjusted energy measurements of detection events occurring simultaneously in two or more pixels to energy spectra of detection events occurring in single pixels. Thus, the processor may combine the non-charge-shared events with all charge-shared events corrected by the charge sharing correction factor to create one spectrum with the peak adjusted to V_(peak1).

The combined spectra created in step 1412 will offer accurate spectra with efficiency than achieved using conventional correction methods. Experiments have shown an in increase in efficiency of 40-50% while maintaining accurate energy resolution compared to other methods.

In various embodiments, the operations in steps 1402-1408 may be performed during a calibration procedure, such as during manufacture of the radiation detector and/or during service of a gamma camera using a gamma source with a known gamma ray energy and flux, while the operations in steps 1410 and 1412 are performed during imaging operations of the gamma camera.

FIG. 14B illustrates another method 1450 for calibrating pixel radiation detectors and adjusting the output of such detectors to account for charge sharing effects according to another embodiment. The method 1450 may be implemented by a processor of a computing device (e.g., the computer 112 of FIG. 1 or the computing device 1500 of FIG. 15).

In the method 1450 the steps 1402 to 1406 may be performed as described above for the method 1400.

In step 1452, the processor may calculate the charge sharing correction factor (CSCF) using the formula (V_(peak1)−V_(peak2))/V_(peak2). Typically this will be about 10-15%, but may be larger for detectors with a large inter-pixel gap with respect to the pixel pitch. Depending upon the inter-pixel gap and the quality of the surface passivation, this number can vary from 0 to 50%.

In various embodiments, the operations in steps 1402-1406 and 1452 may be performed during a calibration procedure, such as during manufacture of the radiation detector and/or during service of a gamma camera using a gamma source with a known gamma ray energy and flux. The operations in steps 1410 and 1412 are performed as described above for the method 1400 during imaging operations of the gamma camera.

The calibration operations illustrated in the embodiment methods 1400 and 1450 may be performed after manufacturing on a per detector basis in order to accommodate differences in inter-pixel gap charge loss resulting from differences in surface passivation that may occur from fabrication lot to fabrication lot, from detector to detector within a fabrication lot. Alternatively, the calibration operations illustrated in the embodiment methods 1400 and 1450 may be performed after detectors have been assembled into a gamma camera, such as part of initial and/or periodic calibrating the camera and imaging system. The calibration operations illustrated in the embodiment methods 1400 and 1450 may be repeated across a range of temperatures at which the detector is expected to operate. Further, the calibration factors determined in steps 1408 and 1452 may be determined for each inter-pixel gap to account for the differences in surface passivation across each detector.

When the calibration operations in steps 1408 and 1452 are performed during or after fabrication, the correction factor(s) determined during calibration testing may be stored in FLASH memory of the detector module as part of steps 1408 and 1452, so that the correction factors are available for use in steps 1410 during operation of the detector. When the calibration operations in steps 1408 and 1452 are performed after assembly of the imaging system (e.g., a SPECT system), the correction factor(s) determined during calibration testing may be stored in memory of an analysis unit (e.g., 110) as part of steps 1408 and 1452, so that the correction factors are available for use in steps 1410 during operation of the imaging system.

The various embodiments (including, but not limited to, embodiments described above with reference to FIGS. 14A and 14B) may also be implemented in computing systems, such as any of a variety of commercially available servers. An example server 1500 is illustrated in FIG. 15. Such a server 1500 typically includes one or more multicore processor assemblies 1501 coupled to volatile memory 1502 and a large capacity nonvolatile memory, such as a disk drive 1504. As illustrated in FIG. 15, multicore processor assemblies 1501 may be added to the server 1500 by inserting them into the racks of the assembly. The server 1500 may also include a floppy disc drive, compact disc (CD) or digital versatile disc (DVD) disc drive 1506 coupled to the processor 1501. The server 1500 may also include network access ports 1503 coupled to the multicore processor assemblies 1501 for establishing network interface connections with a network 1505, such as a local area network coupled to other broadcast system computers and servers, the Internet, the public switched telephone network, and/or a cellular data network (e.g., CDMA, TDMA, GSM, PCS, 3G, 4G, LTE, or any other type of cellular data network).

Computer program code or “program code” for execution on a programmable processor for carrying out operations of the various embodiments may be written in a high level programming language such as C, C++, C#, Smalltalk, Java, JavaScript, Visual Basic, a Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages. Program code or programs stored on a computer readable storage medium as used in this application may refer to machine language code (such as object code) whose format is understandable by a processor.

The present embodiments may be implemented in systems used for medical imaging, Single Photon Emission Computed Tomography (SPECT) for medical applications, and for non-medical imaging applications, such as in baggage security scanning and industrial inspection applications.

Charge sharing effects in pixel radiation detectors may cause efficiency variations and spectral degradation. In a photon counting system, like a SPECT system, such events can be missed or double-counted, depending on the detector settings. The effect depends on the pixel geometry, detector thickness, electric field and the size of the charge cloud spreads as it drifts towards the anodes. In spectroscopic systems, such as SPECT, charge-sharing events are even more harmful as they disturb readings of the gamma-ray photons. Charge sharing, if left uncorrected, may lead to lower detector efficiency, increased spectrum tail and decreased energy resolution.

The various embodiments overcome these issues caused by charge sharing in pixel radiation detectors by providing a method that properly treats the charge-sharing phenomena by precise calibration of CZT pixel radiation detectors. The methods of various embodiments apply in particular to spectroscopic applications, and for systems that use small-pixel detectors in SPECT. In particular, various embodiments include measuring radiation energy spectra by a pixel radiation detector capable of registering simultaneous, coincident detection events occurring in two or more pixels, adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor, and determining a corrected energy spectra by adding the adjusted energy measurements of detection events occurring simultaneously in two or more pixels to energy spectra of detection events occurring in single pixels. In some embodiments, determining the charge sharing correction factor may include creating a first energy spectra for detection events occurring in single pixels and determining its peak value Vpeak1, creating a second energy spectra for detection events occurring simultaneously in two or more pixels and determining its peak value Vpeak2, and calculating the charge sharing correction factor as (Vpeak1−Vpeak2)/Vpeak2. In some embodiments, adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor may include multiplying measured energies of detection events occurring simultaneously into more pixels by a factor of one plus the charge sharing correction factor.

While the disclosure has been described in terms of specific embodiments, it is evident in view of the foregoing description that numerous alternatives, modifications and variations will be apparent to those skilled in the art. Each of the embodiments described herein may be implemented individually or in combination with any other embodiment unless expressly stated otherwise or clearly incompatible. Accordingly, the disclosure is intended to encompass all such alternatives, modifications and variations which fall within the scope and spirit of the disclosure and the following claims. 

What is claimed is:
 1. A method for correcting spectra measured by a pixel radiation detector to account for inter-pixel charge sharing effects, comprising: measuring radiation energy spectra by a pixel radiation detector capable of registering simultaneous, coincident detection events occurring in two or more pixels; adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor; determining a corrected energy spectrum by adding the adjusted energy measurements of detection events occurring simultaneously in two or more pixels to energy spectra of detection events occurring in single pixels; and determining the charge sharing correction factor by: creating a first energy spectra for detection events occurring in single pixels and determining its peak value V_(peak1); creating a second energy spectra for detection events occurring simultaneously in two or more pixels and determining its peak value V_(peak2); and calculating the charge sharing correction factor as (V_(peak1)−V_(peak2))/V_(peak2).
 2. The method of claim 1, wherein adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor comprises multiplying measured energies of detection events occurring simultaneously into more pixels by a factor of one plus the charge sharing correction factor.
 3. A method of calibrating a pixel radiation detector to account for inter-pixel charge sharing effects, comprising: measuring radiation energy spectra from a radiation source having a known gamma photon energy by the pixel radiation detector using electronics capable of registering simultaneous, coincident detection events occurring in two or more pixels; recording energies measured in adjoining pixels for detection events occurring simultaneously in two or more pixels; and determining a charge sharing correction factor based upon the radiation source known gamma photon energy and recorded energies measured in adjoining pixels for detection events occurring simultaneously in two or more pixels, wherein the method is performed as part of manufacturing the pixel radiation detector.
 4. The method of claim 3, wherein determining a charge sharing correction factor based upon the radiation source known gamma photon energy and recorded energies measured in adjoining pixels for detection events occurring simultaneously in two or more pixels comprises: creating a first energy spectra for detection events occurring in single pixels and determining its peak value V_(peak1); creating a second energy spectra for detection events occurring simultaneously in two or more pixels and determining its peak value V_(peak2); and calculating the charge sharing correction factor as (V_(peak1)−V_(peak2))/V_(peak2).
 5. The method of claim 3, further comprising storing the charge sharing correction factor in memory associated with the pixel radiation detector.
 6. A Single Photon Emission Computed Tomography (SPECT) imaging system, comprising: a pixel radiation detector; and an analysis unit configured to receive data from the pixel radiation detector and output analyzed data to a digital image processing computer, wherein the analysis unit is configured to perform operations of: adjusting energy measurements of detection events occurring simultaneously in two or more pixels by a charge sharing correction factor; and determining a corrected energy spectrum by adding the adjusted energy measurements of detection events occurring simultaneously in two or more pixels to energy spectra of detection events occurring in single pixels, wherein determining the corrected energy spectrum comprises: creating a first energy spectra for detection events occurring in single pixels and determining its peak value V_(peak1); creating a second energy spectra for detection events occurring simultaneously in two or more pixels and determining its peak value V_(peak2); and calculating the charge sharing correction factor as (V_(peak1)−V_(peak2))/V_(peak2). 